Solve for $x$ : $x^2 - 17x + 70 = 0$
Explanation: The coefficient on the $x$ term is $-17$ and the constant term is $70$ , so we need to find two numbers that add up to $-17$ and multiply to $70$ The two numbers $-7$ and $-10$ satisfy both conditions: $ {-7} + {-10} = {-17} $ $ {-7} \times {-10} = {70} $ $(x {-7}) (x {-10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x -10) = 0$ $x - 7 = 0$ or $x - 10 = 0$ Thus, $x = 7$ and $x = 10$ are the solutions.